Mathematicians and the Market

Geoff Davis, Mathematics Department, Dartmouth College

Introduction

Young mathematicians have been facing dismal
job prospects throughout the nineties. The fall unemployment rate for new Ph.D.s
in the U.S., as measured by the AMS-IMS-MAA Annual Survey (Second Report), rose
from 2.5% in 1990 to a peak of 13.2% in 1994*. Unemployment rates
have fallen moderately since to the current level of 9.5% in 1996. This is not
the first time that labor market problems have plagued mathematics. The early
seventies saw a similar situation. The Ph.D. glut of the seventies had
far-reaching consequences. It led to drastic funding cutbacks in graduate
education from which it took nearly 15 years to recover. The effects of the
present labor market woes are already visible and dramatic, and they will
certainly be damaging to mathematics in the long term. As we document below, the
high unemployment rates facing recent Ph.D.s are only the tip of the
iceberg.

A variety of external factors have contributed
to the present situation. Changes in funding levels, recent immigration
legislation, and the finances of higher education have all contributed to the
present problems faced by Ph.D.s. It is all too easy to blame outside forces
beyond our control for our troubles, however. The truth is that we in the
mathematics community share the responsibility for the current employment
crisis. Our community has dramatically expanded production of Ph.D.s without
questioning whether there was sufficient demand for our product. Even after five
years of serious and sustained employment problems, we have done little to adapt
to the changes in the market for mathematicians.

Our community has failed to provide answers to
the problems facing recent graduates. What is more, after five years we have
barely begun asking the right questions in a systematic way. What are the
effects of the current labor market problems on the mathematics community as a
whole? What forces have contributed to these problems? What are effective
remedies? We address each of these questions, providing partial answers when
data exists, and pointing out the key gaps in our current understanding. We
conclude by describing some specific steps that the mathematical societies can
take to improve the current labor market situation for mathematics
Ph.D.s.

How have employment problems affected the mathematics community as a whole?

The high unemployment rate of new Ph.D.s in
the fall after graduation is a familiar fact in our community. However, the
current labor market problems have had pernicious effects on all levels of
mathematics, and these are considerably less well known. We first examine these
effects to show just how damaging the labor market problems have
been.

Unemployment and Underemployment

Consider the unemployment information
presented in the AMS-MAA-IMS Annual Survey. The 8.1% reported unemployment rate
is an important measurement, but it hides as much as it reveals. First of all,
the Annual Survey figures systematically underestimate total unemployment rates
by not taking into account unemployment among doctorates outside the U.S. The
8.1% figure is the ratio of unemployed doctorates known to be in the U.S. to the
total number of doctorates whose whereabouts are known. If we compute instead
the ratio of unemployed doctorates in the U.S. to the total number of doctorates
known to be in the U.S., we obtain a more relevant U.S. unemployment rate of
9.5%.

The reported unemployment rate is distorted by
a second factor as well. Some departments provide a form of welfare for Ph.D.s,
offering temporary positions to graduates who are unable to find work elsewhere.
It is not known how widespread this practice is, but the fact that nearly one
quarter of Ph.D.s hired by U.S. doctoral degree-granting programs in 1996 (6.5%
of all Ph.D.s known to be in the U.S.) were hired by the departments that
granted them their degrees is telling. Furthermore, 3.8% of the employed Ph.D.s
were working part-time, with at least 20% of these part-time employees still
looking for full-time work. Even in the improved conditions of 1996, on the
order of 16% of Ph.D.s in the U.S. were either unemployed or underemployed,
twice the reported rate of unemployment.

The decrease in the U.S. unemployment rate
from 12.8% in 1995 to 9.5% in 1996 is certainly encouraging. However, the
simplest explanation for the fact that 38 fewer Ph.D.s were still looking for
work in the U.S. in the fall of 1996 than in 1995 is that there were 73 fewer
Ph.D.s granted in 1996 than 1995.

Little is known about what happens to Ph.D.s
beyond the first year after obtaining their degrees. In 1995 the AMS conducted a
study of the employment status of the class of 1991 two years after they
obtained their degrees.In the fall after their graduation, 6.1% of
the 1991 Ph.D.s in the U.S. were unemployed. Those who obtained short-term
positions had a much harder time during their second round of job seeking. Of
the 1991 Ph.D.s employed in U.S. academic institutions who changed jobs, 20%
were unemployed in the fall of 1993. There has been no follow-up on this
disturbing finding.

Erosion of Opportunities

175 years ago economist David Ricardo
observed, "labor is dear when it is scarce and cheap when it is plentiful." Not
surprisingly, an 8% decline in real 9-month teaching and research salaries for
new Ph.D.s has accompanied the increase in Ph.D. supply between 1989 and 1996.
Moreover, a more subtle change is occurring. There is a hidden downward trend in
total compensation for new Ph.D.s that is occurring as the types of jobs
held by new Ph.D.s change. New Ph.D.s in academia are increasingly employed as
temporary rather than tenure-track employees. Between 1990 and 1995, the number
of full-time non-tenure-eligible faculty in traditional math departments (Groups
I-III) increased by 37%. At the same time the number of tenure-track faculty
fell by 27%. Temporary faculty now comprise 56% of all non-tenured faculty in
traditional math departments.

In addition to having no job security,
temporary workers receive fewer benefits than tenure-track employees do.
Furthermore, temporary employment delays entry onto the tenure-track salary
ladder. Each year on postdoctoral-level wages delays the transition to assistant
professor salary levels by one year, and results in one less year as a full
professor. Thus, total lifetime earnings of new doctorates have been
depressed.

An increase in the amount of time required to
earn a Ph.D. represents a second form of reduction in lifetime earnings.
National Research Council data show that the median time to degree*
has increased from 6.5 to 8.0 years between 1982 and 1993. The current Ph.D. oversupply
aggravates this problem by providing strong incentives for students to remain in
graduate school for longer and longer periods of time in the hope that
additional time for research will make them more marketable.

At present, no information is available on the
average amount of time that new doctorates spend in temporary positions. Little
is known about average total compensation for postdoctoral researchers or the
effect of temporary positions on the time to tenure. Such information is
essential for obtaining a true measure of the health of the
profession.

Declining Enrollments

The opportunity costs of graduate school have
become increasingly difficult for prospective students to justify as the
prospects and compensation for Ph.D.s decline and the time to degree increases.
The median salary this year for new math Ph.D.s in 9-month teaching and research
positions, the most common type of academic position held by new Ph.D.s, is
$36,000. This is less than the $37,500 to $41,400 starting salaries commanded by
1996 bachelors degree recipients in electrical, computer, or chemical
engineering. To our most
talented students, the mere $6,000 difference in starting salary over that for
mathematics bachelor’s degree holders does not make a strong economic case for
years of intensive postbaccalaureate training amidst deteriorating employment
conditions.

There is considerable evidence that labor
market considerations play a strong role in determining educational and career
choices for young people. In the words of Ed David, author of the David reports,
"That [mathematics education is one of the best preparations for almost any
career] may very well be true, but the students must believe that, or we won't
have any students. And at the moment they don't appear to believe it." A recent
AMS study bears this out. Applications to graduate programs in mathematics fell
by 30% between the fall of 1994 and the fall of 1996.
Moreover, the number of first year full-time graduate students in traditional
math departments (Group I, II, and III schools) declined by roughly 23% between
1991 and 1996. The students we are losing are those with sufficient breadth of
talent to pursue other opportunities. We are driving out intellectual diversity
at precisely the time we need it most.

An anecdote of Harvard labor economist Richard
Freeman puts these trends into perspective. Freeman was invited to speak to the
physics department at the University of Chicago during the height of the physics
employment crisis in the seventies. He writes,

When I finished the presentation, the
chairman shook his head, frowning deeply…. "You’ve got us all wrong," the
chairman said gravely. "You don’t understand what motivates people to study
physics. We study for love of knowledge, not for salaries and jobs." "But…," I
was prepared to give … arguments about market incentives operating on some
people on the margin, when the students – facing the worst employment prospects
for graduating physicists in decades – answered for me with a resounding chorus
of boos and hisses. Case closed.

What Freeman does not mention is his response
to assertions such as those made by the chairman, something to the effect of,
"Terrific. If that’s true, a 5% voluntary pay cut by senior scientists should be
enough to prop up the market for entering physicists." This may have made his
point.

Loss of Departmental Autonomy?

University administrators are under
considerable pressure to cut costs in the current climate of fiscal retrenchment
in academia. In the past, cost-cutting mechanisms such as departmental
downsizing, faculty wage freezes, and increased teaching loads have carried with
them the risk of the loss of top faculty members and the inability to recruit
new talent. Might long lines of talented, inexpensive, and job-hungry new
doctorates standing ready to fill any available position embolden institutions
to employ such measures? The recent attempts by the Regents of the University of
Minnesota to eliminate tenure and by the University of Rochester to eliminate
their mathematics graduate program are certainly
suggestive.

What forces have contributed to the present labor market problems?

The current job crunch for math Ph.D.s has two
basic causes: a rapid increase in supply accompanied by a large decrease in
demand. Both are important for understanding the present
situation.

Increased Supply

769 mathematics Ph.D.s were conferred in 1985.
Ten years later, that number had grown to 1226, an increase of nearly 60%. The factors influencing departmental determinations of
Ph.D. production levels have been examined in a series of faculty interviews
conducted by William Massy of the Stanford Institute for Higher Education
Research. Massy and co-author Charles Goldman report that

...faculty express concern about the
labor market for Ph.D.s and will do what they can to place their own
students—but their concern does not lead to adjustments in doctoral student
intakes. Faculty tend to believe that more scientifically-trained manpower is
better than less, and that job opportunities will materialize somehow. In any
case, the department’s short-run requirements for inexpensive research and
teaching labor, and the desire of faculty to replicate their own skills, is of
stronger relevance to admissions decisions than the more abstract and distant
concept of labor market balance.

Massy and Goldman found that the primary
factors used to determine Ph.D. program size are the number of faculty advisors
available, the number of teaching assistants needed for staffing classes, the
amount of research money available for funding assistantships, and the quality
of the applicant pool. The recent increase in Ph.D. production has been driven
by increases in two of these factors: funding levels and the size of the foreign
applicant pool.

Increased Funding for Graduate Education

Federal support for the mathematical sciences
increased by 34% in constant dollars between 1984 and 1989 following the release
of the David Report in 1984. A substantial fraction of
these new resources were used for funding graduate education. The David Report sought to
reinstate funding for graduate education that was cut during the Ph.D. job
crisis of the seventies. Ironically, in so doing, it has contributed to a
repetition of the oversupply of Ph.D.s that led to the loss of funding in the
first place.

Increased Immigration

A sizable increase in the foreign student
population has also contributed to the expansion of Ph.D. production. The number
of Ph.D.s granted to non-citizens nearly doubled between 1985 and 1995, and this
increase has accounted for roughly two thirds of the growth in Ph.D. production
over this time period. The presence of a large foreign student population in and
of itself is no cause for concern. Indeed, a wide variety of international
educational exchange programs have been designed to build ties between the
scientific communities in U.S. and other countries, to promote cultural
exchange, and to provide valuable training to the scientific workforce of less
developed countries. Foreign exchange students who leave the U.S. after
graduation have no impact on the U.S. labor market. The relevant question here
is not how many non-citizen Ph.D.s are granted but how many of these students
remain in the U.S. after graduation.

The Annual Surveys do not provide data on the
post-graduation statuses of non-citizen doctorates. However, we can obtain a
lower bound on the number in the U.S. in the fall after graduation by assuming
that all new Ph.D.s known to be outside the U.S. are non-citizens. Figure 4
below compares the number of non-citizen Ph.D.s granted each year to the number
of Ph.D.s known to be outside the U.S. in the fall after earning their degrees.
At least 44% of non-citizen Ph.D.s were known to be in the U.S. in the fall
after graduation in 1985. In contrast, the 1995 figure was 67%. Although the
number of Ph.D.s granted to non-citizens has increased substantially over the
past decade, the total number of new Ph.D.s employed outside the U.S. has
remained nearly constant.

The influx of foreign Ph.D.s does not appear
to be the sudden result of one-time political events such as the breakup of the
Soviet Union and the post-Tiananmen Square exodus from China. On the contrary,
as Figure 4 shows, the increase in the graduate non-citizen population has taken
place gradually since the early eighties, well before these events. The
Immigration Act of 1990 contains provisions, included at the behest of such
organizations as the Association of American Universities to counteract
projected Ph.D. shortages, which give university employers special privileges in
hiring non-citizen faculty members. This legislation may well have contributed
to an increase in immigration.

The Quest for Prestige?

Data collected by the National Research
Council show that perceived program quality, as measured by NRC faculty quality
ratings, is strongly linked with program size. Out of seventeen objective
departmental criteria measured, the study found the quantity most strongly
correlated with perceived faculty quality was a measure of annual Ph.D.s
production (r = 0.73). The correlation between faculty quality and the total
number of students in the program is also relatively large (r = 0.63). The
precise reason for this link is unknown. Perhaps a large program size, a
"critical mass," is necessary to attract high quality faculty members. Having
graduate students is viewed by faculty as a necessary condition for research
productivity (and therefore program quality), and as a result faculty express
strong resistance to the idea of decreasing enrollments within their own
programs. Alternatively, perhaps having high faculty quality leads to expansion
through increased access to grant money for funding students. In either case,
the link between program size and perceived quality suggests that the drive for
increased program quality may result in a system-wide tendency to expand Ph.D.
production regardless of job market conditions.

Decreased Demand

Decreased Funding for Faculty Positions

While the supply of Ph.D.s continued to increase through the
early nineties, demand fell. The number of positions offered in math departments
declined by a third between 1989 and 1994. Much of this decrease can be
attributed rapidly rising costs for higher education accompanied by cuts in
government funding during that time period. Combined federal and state support
for public higher education fell by 8.8% between 1980 and 1993 due in part to
rising costs of Medicaid. Federal support for private institutions fell by 4%
during the same period.

For the past several years, the science community has been
tremulously following every nuance of the annual NSF budget negotiations. To be
sure, these negotiations are important ones: NSF funding levels determine the
availability of research assistants, summer salaries, and the speed of our
computers. Even more important to our community is the financial health of the
overall higher education system, yet to this central issue we pay relatively
little attention.

Faculty Demographics

Examination of the age distributions of mathematics departments
shows a demographic bulge due to the large cohort of mathematicians hired during
the late sixties and early seventies. The presence of this large cohort of
mathematicians in their late fifties and early sixties, the recent elimination
of mandatory retirement, and the current reduced hiring of junior tenure-track
faculty all suggest that mathematics departments are aging. What are the effects
of these shifting demographics? In a recent book, Professor Andrew Hacker puts
it bluntly: "Every full professor who refuses to retire is preventing several
young scholars from beginning their careers." We need to understand how
departmental demographics are evolving and what the consequences of any changes
will be.

Delayed Market Feedback

Why have market forces not corrected the
present job market problems? Market forces do appear to be in operation:
first-year enrollments to graduate programs have fallen dramatically since the
current job market woes began. The problem is one of timing. There is a lengthy
delay between changes in first-year enrollments and the resulting changes in the
Ph.D. supply. This type of delayed feedback system, called a "cobweb supply
model", is commonly used in economics for studying markets for agricultural
commodities. The result of the delay is oscillatory behavior in the system. When
market conditions are good, enrollments increase. Many years later, these
increased enrollments lead to an oversupply of Ph.D.s. The resulting poor market
causes enrollments to fall, which leads to shortage conditions years later, and
so on.

The period of the oscillation that results
from the delayed feedback system is twice the amount of time between the
decision to attend graduate school and the completion of a doctorate. Estimates
of the median amount of time required to obtain a doctorate in mathematics range
from 6.9 years to 8.0 years. There is an additional lag since the decision to
attend graduate school must be made at least a year before enrollment to allow
time for applying to schools. Hence this delayed feedback model predicts an
oscillation in Ph.D. supply with a period of roughly 16 to 18 years. This is
consistent with recent history: the Ph.D. supply peaked in the early seventies,
bottomed out in the mid-eighties, and peaked again in the early nineties.

First steps towards solving our chronic labor market problems

Assessing Supply and Demand: A "State of the Union" Report for Mathematics

The discussion above suggests that an
important factor in the current labor market problems is the way the supply of
doctorates is currently regulated. The mathematical societies do not have the
power to impose production quotas. Even if they did, such quotas would most
likely create many more problems than they would solve. An important step that
the societies can take instead is to provide sufficient information for
prospective students, departments, and funding agencies to make more rational
decisions regarding enrollments.

1. The mathematical societies should
commission an annual report that analyzes trends affecting the supply of and
demand for Ph.D.s five to ten years into the future.

If departments, students, and funding agencies
are to make rational enrollment and funding decisions, they will need
information about anticipated market conditions. The societies can help all
three parties to make informed choices by providing an annual report outlining
major trends affecting the supply and demand for Ph.D.s. This report should
include a discussion of the effects of current and proposed legislation,
demographic changes, political events abroad that affect immigration, trends in
industry, and so on. The effort in preparing the report could be shared with
scientific societies in other disciplines.

The report should be supplemented with
projections of Ph.D. supply and demand. The time frame of the projections should
be such that prospective students will have an idea about market conditions at
the time of their graduation. Projecting supply over such a limited time frame
is relatively straightforward given up-to-date information on current enrollment
levels, attrition rates, and time to degree. See, for example, Freeman, 1989.
Given the relatively strong historical correlation between the supply of Ph.D.s
and the unemployment rate (r = 0.82), it is likely that supply estimates would
prove to be quite valuable in assessing future market
conditions.

Projecting demand is a much more difficult
than projecting supply. The point, however, is not to provide a perfect
forecast, but rather to provide informed estimates of the effects of various
demand-side forces. For example, an estimate of the effects the recently passed
five-year, $48 billion dollar tax incentive package for higher education on the
demand for Ph.D.s in research-intensive versus teaching-intensive institutions
would be quite valuable in assessing the need for training in teaching skills.
The societies should draw upon outside expertise, especially that of labor
market economists, in assessing the market conditions that will face new
doctorates.

1(a) All analyses of supply and demand
should be formulated in conjunction with a stringent review process to avoid
potential conflicts of interest.

The notion that the supply of and demand for
scientists and mathematicians can be predicted at all has been called into
question by an infamous NSF study that projected a cumulative shortfall of
675,000 scientists and engineers between 1991 and 2006. A follow-up article by one of the study’s authors
predicted a cumulative shortfall of 153,600 science and engineering Ph.D.s
between 1995 and 2010. Despite strong criticism of the study’s methodology from
experts both inside and outside the NSF, the study was broadly distributed to
policy makers. Howard Wolpe, chairman of a 1992 congressional investigation into
the release of the study, writes, "In 1987 the NSF adopted a plan to double its
budget in five years. There is no doubt in my mind that this shoddy science was
knowingly disseminated by the federal government’s premier scientific agency to
further the attainment of this goal." Wolpe’s subcommittee found that criticism
of the study "was ignored and even suppressed within the Foundation…. The NSF
publications office … prevented the study from being printed as an official NSF
document for over two years because of questions about credibility, until the
director finally forced its publication." The lesson to be taken from the NSF
study is not that the future is completely unforeseeable. Rather, it is that
great care must be taken in light of the potential for serious conflicts of
interest involved in projecting Ph.D. supply and demand.

1(b) The mathematical societies should
re-evaluate the type of information collected in their annual departmental
surveys. They should update assessments of future supply and demand regularly as
new data becomes available.

In 1990 the David II Report recommended
substantial expansions in mathematics Ph.D. production just months before the
bottom fell out of the job market for new Ph.D.s. The report justified its
recommendations using projections made by Bowen and Sosa.The trouble with these
projections is that although they were carefully constructed and well
documented, they relied on data and assumptions that were out of date. Several
assumptions about Ph.D. production rates and immigration levels used by Bowen
and Sosa were clearly wrong by the time of the David II Report’s release. For
example, the 1987 Ph.D. production figures used for projecting future Ph.D.
supply were old data, reflecting enrollment decisions made some 5 to 8
years earlier. First-year graduate enrollment figures reveal future changes in
Ph.D. supply much more quickly than do graduation numbers. Had Bowen and Sosa
had access to such enrollment data, their projections for the nineties may well
have been quite different.

The lesson is that assessments of supply and
demand need to be made on an ongoing basis, and these assessments should be
revised as new information becomes available. Projections of future market
conditions will require much more detailed data on attrition rates, time to
tenure, departmental demographics, and the hiring of non-citizen doctorates than
is currently collected. The societies should determine the data needs of supply
and demand models and should adjust their data gathering accordingly. These data
should be made public to facilitate research on the labor market for
scientists.

Assessing Program Effectiveness

The oversupply of Ph.D.s is not the only
problem facing recent doctorates as they seek employment. A recent Bureau of
Mathematical Sciences study of graduate programs found that "Many doctoral
students are not prepared to meet undergraduate teaching needs, establish
productive research careers, or apply what they have learned in business and
industry." Furthermore, higher education is changing rapidly as student bodies
become more heterogeneous in terms of ethnicity, income, age, and levels of
student preparation. In a recent essay in the New York Times Magazine
about these changes on campus, Professor Louis Menand writes,

The academic job market is bad
everywhere, but the reason often given by elite universities – which is that
there are too many "lesser ranked" doctoral programs – is disingenuous. In many
cases, the top-ranked programs are the ones having trouble placing their
graduates. The reason may be that their students’ training is perceived as too
specialized, and their teaching experience as too narrow, by many of the schools
where jobs are available.

What kinds of training programs are effective
for various types of departmental missions? What is the best way to prepare
students for careers at small liberal arts colleges? For careers at research
universities? For careers in industry? If mathematics doctorates are to obtain
employment of the type that they seek in the rapidly changing workplace, it is
imperative that they receive the proper training. "My experience convinces me
that graduate education can be changed to reflect the real needs of the
profession, and the changes would not even have to be far-reaching. But we will
have to be prepared to give up the idea that departments and schools have only
minimum collective responsibility for the outcome," writes former Stanford
president Donald Kennedy.

2. The mathematical societies should
collect and make publicly available information on graduate placement rates for
all Ph.D. programs.

A recent National Research Council report
recommends that information on graduate placement rates for individual programs
be gathered by the research community and made available on the Internet.
Publicly available placement data would provide an invaluable measure of program
effectiveness in preparing students for a wide variety of
careers.

The outcome data collected for the new ratings
would make it possible for the first time to evaluate program characteristics
based on empirical considerations. For example, increasing the breadth of
education has been widely advocated as a method for improving the job prospects
of Ph.D.s. However, a number of mathematicians have raised concerns about the
tradeoff between breadth and depth. Is breadth or depth more important, and in
what contexts? This is a question best answered by looking at data on outcomes.
Outcome data would serve to highlight a broad range of program characteristics
that contribute to students’ preparation for successful careers.

Public outcome data would enable prospective
students to make more informed choices about what graduate school to attend.
They would steer students toward programs with graduate outcomes closely
matching students’ own career aspirations. Outcome data would also provide
students with realistic career expectations. Outcome data are but one factor
among many for students to consider in choosing a graduate program. Other
information that would be helpful includes data on time to degree, degree
completion rates, and financial aid.

A key issue in the gathering placement data is
that of how to assess graduate outcomes. The fact that a program’s graduates are
employed does not indicate whether they are employed in jobs appropriate for
their level of training. Who decides what is a positive graduate outcome? The
answer is simple: we should turn to the graduates themselves for answers.
Measures of the success of graduate outcomes should be based on responses of
recent graduates to questions regarding their job satisfaction, the degree to
which their training prepared them for their current positions, and the extent
to which they use skills acquired in graduate training in their current
positions. No value judgment needs to be made on the relative merits of
industrial versus academic employment except by the doctorates
themselves.

Conclusion

The environment in which mathematicians
operate is changing rapidly. If our community is to govern itself in a
responsible manner, it is imperative that we understand and adapt to these
changes. Our reluctance to examine difficult issues such as the determination of
enrollment levels, immigration, changing faculty demographics, and the
effectiveness of various types of training programs neither makes these issues
disappear nor mitigates their effects. The mathematical societies have the
opportunity to take a strong leadership role here. Better information on the
market for Ph.D.s and an assessment of the effectiveness of different types of
training programs are not a cure-all prescription, but they do represent an
important first step. We in the mathematics community need to take a more active
role in solving our current labor market problems and in preventing future ones.
The future of the profession and the next generation of mathematicians depend
upon it.

Acknowledgments

The author would like to thank Sue Minkoff,
Eric Weinstein, and many others for helpful feedback and comments. He also
thanks the Digital Signal Processing group at Rice University for their generous
hospitality during the writing of this
paper.